THE EXTENDED FINITE ELEMENT METHOD BASED ON THE STATE VECTOR

The displacement field and the stress field are computed by a semi-analytical method based on the Hamilton canonical equation, and the results are found very satisfactory. But when the tip field is considered, the tip field must be more finely meshed. Both the stiffness matrix and the stress field must be calculated anew when the crack propagates, which makes very low resolution efficiency. Based on the extended finite element method, the discontinuity of the crack could be taken care of, to avoid the re-meshing. In order to take a full advantage of the Hamilton system and the extended finite element method, this paper combines them to analyze the fracture problem, such as the calculation of the stress intensity factor and the simulation of the crack propagation. The results from the case analysis demonstrate that the method is feasible.